The Kalman filter receives a series of measurements observed by a system over time, which include noise and other inaccuracies, and produces estimates of unknown variables representing the system. These variables are known as the system state which becomes more accurate and precise over time. The Kalman filter operates recursively on noisy input data and produces an optimal estimate of the system state.
The Kalman filter works in a two-step process. One step is referred to as a prediction step and the other step is referred to as an update step. The prediction step produces estimates of the current state variables of the underlying system. Once the next measurement is observed, which is corrupted by error and noise, the state variables are updated using weighted averages. More weight is given to updates having higher certainty. The Kalman filter can be executed in real time by using only the present input measurements and the previously calculated system state.
The Kalman filter is widely applied to navigation and control of vehicles, in particular aircraft and orbiting satellites. The filter aids vehicles in obtaining better estimates of geographic location, for example, latitude and longitude on the Earth. Moreover, orbiting satellites may include sensors that image the Earth to obtain panoramic views of the Earth. These images are mosaic-ed by registering one image with an adjacent image as the orbiting satellite is in continuous motion. A Kalman filter may be used to obtain knowledge of the geodetic location of a pixel in one image as it relates to the geodetic location of another pixel in an adjacent image.
Conventionally, image registration requires knowledge of the orbit and attitude of the imaging sensor. Typically, such knowledge is obtained by using range sensors and star-fixing measurements to isolate the effects of attitude and nullify the effects of orbit error. A Kalman filter is typically used in the process. A significant component of the complexity in the process is due to the range sensors and the additional computations due to the star-fixing measurements.
As will be explained, the present invention provides an improved Kalman filter that can extract position and attitude information about an imaging sensor orbiting a central body, by using only observations of the central body. No other types of scene observations or scene measurements are needed to obtain this information. As will also be explained, the present invention uses direct observations of the central body as provided in the imaging sensor's native imaging mode. No orbit determination system is required.